The History of Mathematical Proof in Ancient Traditions

(Elle) #1

592 Index


scribal school, 384, 386–7, 390, 405; see also
Babylonian mathematics
scroll, 71–2, 84
Sea island , see Hai dao
Sea mirror of the circle measurements , see
Ceyuan haijing
Sédillot, J.-J., 274
Sédillot, L.-A., 274
self-evidence, 305, 378, 380
separation of ‘Western’ from ‘non-Western’
science, 10, 53, 56, 59, 291
sequence,
direct sequence and reverse sequence,
398–403, 405, 406, 409–10, 412, 415, 417
sequence of operations or calculations,
397–8, 404
see also algorithm, geometric progression
Sesiano, J., 347, 350
sexagesimal place value notation, 384, 388–9
shang chu ‘evaluation division’, 538, 542;
see also division
shapes of fi elds, see tian shi
shaping of a scientifi c community, 4–5, 11
shares, see fen
Shen Kangshen , 423, 485, 486
shi ‘dividend’, 431–4, 459–62, 467–72, 478 
shi ‘schemes’, 539, 544
Shu shu ji yi , 517, 520, 533, 546
Shu xue ‘College of calligraphy’, 521
Shukla, K. S., 487–508
Shuo wen jie zi (dictionary), 511
Sidoli, N., 23–5, 139, 150, 158
silk, 469
simplicity, 435, 442
Simplicius, 76, 85, 121, 131, 134, 296
simplifi cation, 431
of an algorithm, 471
of fractions (‘procedure for simplifying parts’
yuefen shu ), 431, 437, 460–1,
467, 469–70
sinology, 275
Siu Man-Keung , 513, 515, 519–23, 535
Six Codes of the Tang [Dynasty] (Th e), see Ta n g
liu dian
Smith, Adam, 382
Smith, A. M., 304
social context for proof, 18–19, 43, 53, 60–1
development and promotion of one tradition
as opposed to another, 60
interpreting a classic, 47–53, 60, 423–84
professionalization of scientists, 4, 11
rivalry between competing schools of
thought, 1, 29–30, 59

teaching, 11, 44, 53–5, 60
see also mathematical education
Socrates, 298, 300, 303
solids, 427–8
Song dynasty , 510, 513–14, 519, 523–4, 535
Song Qi , 548
Song shi (History of the Song (dynasty)),
532–3, 535
Sonnerat, P., 236, 237, 258
sophists, 296–7
speculative trend, 286, 302, 510
sphere, 453
as real globe, 150, 158–9
Sphere and Cylinder , see Archimedes, works by
spherical geometry, 139, 150–1, 159
Spherics , see Th eodosius
square root, 386, 388, 410–16
Srinivas, M. D., 7, 12, 51, 67, 260, 273, 487, 508
Staal, F., 267, 273
Stache-Rosen, 261, 273
Stamatis, E., 70, 86, 130, 136, 138, 164
standard formulation, 494
starting points, 2, 14, 300, 303–5
debates about starting points in ancient
Greece, 2, 14, 29
see also axiom , defi nition
State University, see Guo zi jian
statics, 298, 304–5
Stedall, J., 288, 550
Stern, M., 279
Strachey, E., 276, 285
strip [reading] of classics [examination], see
tie jing
strip reading [examination], see tie du
style of proof, 25–6
style ‘characterizing distinct civilizations’, 9,
61, 61
styles of practising mathematics, 9, 34–5, 278
distinctiveness of the Western scientifi c style,
1, 9, 10, 56, 291
‘Greek style’, 8–9, 278
‘Indian style’, 278, 281–2, 290
‘intuitive, illustrative and unrefl ected style’,
291
‘Oriental style’, 9, 285
‘systematic and axiomatic–deductive style’, 291
suan ‘counting rods’, 432, 511, 530, 538,
540–4
suan ‘operations with counting rods’, see
toán
Suan fa tong zong , 512, 524, 526, 546
Suanfa tongzong jiaoshi (An
annotated edition of the Summarized
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